[itex]\delta W_t \sim N(0,t)[/itex]. It follows that [itex]E[(\delta W_t)^2]=\delta t[/itex] and [itex]E[|\delta W_t|^3]={\rm const}\times \delta t^{3/2}[/itex]. So third and higher powers of dW are smaller order than dt on average , and therefore vanish if you sum them over a partition and let dt->0.